Find the nonlinear asymptote of the following function fx x

Find the nonlinear asymptote of the following function.

f(x) = (x⁵ + 4x³ + 3x² )/ (x² + 4)

The nonlinear asymptote is y = _____________.

Solution

f(x) = (x⁵ + 4x³ + 3x² )/(x² + 4)

The result is the sum of a proper fraction (-12/(x^3 + 3)) and a cubic function (x^3 + 3).

The cubic function y = x^3 + 3 is the equation of the nonlinear asymptote.